## 
## SIEMENSPRISMAFIT   SIEMENSTIMTRIO     SIEMENSVERIO 
##               58             1185               36

## 
##  CHP  HSC  PNC 
##   36   58 1185

##                   
##                     CHP  HSC  PNC
##   SIEMENSPRISMAFIT    0   58    0
##   SIEMENSTIMTRIO      0    0 1185
##   SIEMENSVERIO       36    0    0

Excluding HSC-SIEMENSTIMTRIO (n=7) for now.

## [1] "Batches:"

## [1] "CHP-SIEMENSVERIO"     "HSC-SIEMENSPRISMAFIT" "PNC-SIEMENSTIMTRIO"

## Analysis of Variance Table
## 
## Response: age
##             Df  Sum Sq Mean Sq F value    Pr(>F)    
## site         2  1012.5  506.27  34.606 2.313e-15 ***
## Residuals 1276 18667.2   14.63                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age is confounded across sites.

##      
##       FEMALE MALE
##   CHP     24   12
##   HSC     37   21
##   PNC    630  555

##      
##          FEMALE      MALE
##   CHP 0.6666667 0.3333333
##   HSC 0.6379310 0.3620690
##   PNC 0.5316456 0.4683544

## 
##  Pearson's Chi-squared test
## 
## data:  df$site and df$sex
## X-squared = 4.8976, df = 2, p-value = 0.0864

1. Harmonization of intracraneal volume (ICV).

2. Harmonization of 145 volumes

3. ICV Normalization of 145 volumes

Harmonization method: ComBat (Johnson and Li (2007), Fortin et al. (2017), (2018)).

1. Harmonization of intracraneal volume (ICV).
   A. As single dataset.
   B. By Splitting data by Males and Females (M/F).

2. Harmonization of 145 volumes
   A. As single dataset.
   B. By splitting data by Males and Females (M/F).
   C. By splitting data by tissues (Tissue).
   D. B + C.

3. ICV Normalization of 145 volumes
   A. No adjustment.
   B. ICV Residualization: Splitting data by Males and Females (M/F).
   C. ICV Residualization: Joint (i.e. no M/F split).
   D. ICV as Covariate.

## Analysis of Variance Table
## 
## Model 1: X702 ~ sex + age + age * sex
## Model 2: X702 ~ sex + age + age * sex + batch
##   Res.Df        RSS Df Sum of Sq      F  Pr(>F)   
## 1   1275 1.9996e+13                               
## 2   1273 1.9786e+13  2 2.099e+11 6.7524 0.00121 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Model 1: ICV ~ sex + age
## Model 2: ICV ~ sex + age + batch
##   Res.Df        RSS Df Sum of Sq      F Pr(>F)
## 1   1276 1.9760e+13                           
## 2   1274 1.9759e+13  2 753810856 0.0243  0.976

Past this point, all reference to ICV refers to ICV harmonized by splitting data by sex (M/F; Option 1B).

M/F lines up residualized WM volumes best.

M/F also performs the best on residualized GM volumes.

Past this point, all reference to ROI refers refers to ROIs harmonized by splitting data by sex (M/F; Option 2B).

For each of the 145 ROI volumes, two models were used:
- Model 1: ROI ~ sex + age + agexsex (+ ICV)
- Model 2: ROI ~ sex + age + agexsex (+ ICV) + batch

Number of models for which batch variables contributes new information is shown below.

##              Raw    Raw (ICV adj)           Combat Combat (ICV adj) 
##               36               43                0                0

ROIs are corrected for ICV with the formula
\[ROI_{adj} = ROI - \beta (ICV - \overline{ICV})\]
where \(\beta\) represents the ICV-ROI slope and \(\overline{ICV}\) is the average ICV of subjects in the cohort used for the correction (Nordenskjöld et al. 2015).

In this presentation, two cohorts (i.e. males and females) are corrected separately. Effects of using only one cohort are also shown.

(Covariance) PCA was performed with (M/F) ICV-corrected volumes. Then GM and WM totals were projected onto PCs 1 and 2.

Dimension 1

##       contr ROI_INDEX               ROI_NAME HEMISPHERE TISSUE_SEG
## 1 28.917845        81  frontal lobe WM right      Right         WM
## 2 28.259090        82   frontal lobe WM left       Left         WM
## 3  9.032425        87 temporal lobe WM right      Right         WM
## 4  8.372905        88  temporal lobe WM left       Left         WM
## 5  7.895716        86  parietal lobe WM left       Left         WM
## 6  7.033472        85 parietal lobe WM right      Right         WM

Dimension 2

##       contr ROI_INDEX                         ROI_NAME HEMISPHERE TISSUE_SEG
## 1 16.751181        38        Right Cerebellum Exterior      Right         GM
## 2 16.216717        39         Left Cerebellum Exterior       Left         GM
## 3  7.259439       142 Right MFG   middle frontal gyrus      Right         GM
## 4  6.548369       143  Left MFG   middle frontal gyrus       Left         GM
## 5  3.364917       169             Left PCu   precuneus       Left         GM
## 6  3.066817       168            Right PCu   precuneus      Right         GM

Note: Blue lines denote supplementary projections.

Sex differences are retained after ICV-residualizing by sex (M/F Residualization).

Alternatively, GM loses contr. toward Dim 2 and sex differences are eliminated if ICV is residualized irrespective of sex (i.e. Joint Residualization).

In parentheses: ICV normalization method.

<Insert references for Combat and ICV-normalization.>